20220813, 20:22  #375 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}·73 Posts 
Integers b>=2 sorted by A062955(b):
2 (1), 3 (4), 4 (6), 6 (10), 5 (16), 8 (28), 7&10 (36), 12 (44), 9 (48), 14 (78), 11 (100), 18 (102), 15 (112), 16 (120), 13 (144), 20 (152), 24 (184), 22 (210), 30 (232), 21 (240), 17 (256), 26 (300), 19&28 (324), 36 (420), 27 (468), 25 (480), 23 (484), 42 (492), 32 (496), 34 (528), 40 (624), 33 (640), 38 (666), 48 (752), 29 (784), 35 (816), 44 (860), 31 (900), 39 (912), 60 (944), 54 (954), 50 (980), 46 (990), ... Integers b>=2 sorted by number of minimal primes (starting with b+1) base b: (not sure if 26 and 28 are before 17 and 21) 2 (1), 3 (3), 4 (5), 6 (11), 5 (22), 7 (71), 8 (75), 10 (77), 12 (106), 9 (151), 18 (549), 14 (650), 11 (1068), 15 (1284), 16 (2346~2347), 30 (2619), 13 (3195~3197), 20 (3314), 24 (3409), 22 (8003), 17 (10405~10428), 21 (13373~13395), ... Integers b>=2 sorted by length of largest minimal prime (starting with b+1) base b: 2 (2), 3&4 (3), 6 (5), 7 (17), 10 (31), 12 (42), 5 (96), 15 (157), 8 (221), 9 (1161), 18&20 (6271), 24 (8134), 14 (19699), 22 (22003), 30 (34206), 11 (62669), ... These three sequences are conjectured to be similar, the integers b = 7 and b = 15 for the third sequence is relatively small since they (as well as b = 3) are highweight bases (like CRUS bases R7, R15, S7, S15, they are highweight bases), i.e. they are very "primeful", while b = 5 and b = 8 and b = 11 and b = 14 are relatively large, since they are lowweight bases (like CRUS, bases == 2 mod 3 are lowweight bases), although this does not hold for b = 20, which is also == 2 mod 3 bases b such that the number of minimal primes (starting with b+1) base b is in given range: 1: 2 2: none 3~4: 3 5~8: 4 9~16: 6 17~32: 5 33~64: none 65~128: 7, 8, 10, 12 129~256: 9 2^8+1~2^9: none 2^9+1~2^10: 18, 14 2^10+1~2^11: 11, 15 2^11+1~2^12: 16, 30, 13, 20, 24 2^12+1~2^13: 22 2^13+1~2^14: 17, 21, ... bases b such that the length of largest minimal prime (starting with b+1) base b is in given range: 1: none 2: 2 3~4: 3, 4 5~8: 6 9~16: none 17~32: 7, 10 33~64: 12 65~128: 5 129~256: 15, 8 2^8+1~2^9: none 2^9+1~2^10: none 2^10+1~2^11: 9 2^11+1~2^12: none 2^12+1~2^13: 18, 20, 24 2^13+1~2^14: none 2^14+1~2^15: 14, 22 2^15+1~2^16: 30, 11, ... Last fiddled with by sweety439 on 20221002 at 05:05 
20220813, 20:35  #376  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
Quote:
Base 5: aliquot sequence starting with product home prime sequence starting with product inverse home prime sequence starting with product greatest prime factor ^21 sequence starting with product greatest prime factor ^21 sequence starting with sum Base 7: aliquot sequence starting with product home prime sequence starting with product inverse home prime sequence starting with product greatest prime factor ^21 sequence starting with product greatest prime factor ^21 sequence starting with sum Base 8: aliquot sequence starting with product home prime sequence starting with product inverse home prime sequence starting with product greatest prime factor ^21 sequence starting with product greatest prime factor ^21 sequence start with sum Base 10: aliquot sequence starting with product home prime sequence starting with product inverse home prime sequence starting with product greatest prime factor ^21 sequence starting with product greatest prime factor ^21 sequence start with sum Base 12: (no inverse home prime sequence available) aliquot sequence starting with product home prime sequence starting with product greatest prime factor ^21 sequence starting with product greatest prime factor ^21 sequence starting with sum 

20220813, 20:40  #377 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}·73 Posts 
For the interest of "greatest prime factor ^21" sequences:
* N1 primality proving * N+1 primality proving * P1 integer factorization method * P+1 integer factorization method https://oeis.org/A087713 (greatest prime factor of p^21) https://oeis.org/A024710 (the same sequence (start with p=11) of the A087713, which is the greatest prime factor of A024702) https://oeis.org/A024702 ((p^21)/24) https://oeis.org/A084920 (p^21) https://oeis.org/A001248 (p^2) https://oeis.org/A001318 (generalized pentagonal numbers, (n^21)/24) 
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